宽带带通信号的直接采样定理

Sampling Theorem for Wide Band-Pass Signals

对起、止频率为ｆｓ_ｆｅ_的带通信号的直接采样，传统上要求信号是窄带的９即ｆ≥ｆ_ｅ／２），否则只能用经典的Ｓｈａｎｎｏｎ采样定理，以不低于２ｆ_ａ的采样率来采样才能恢复信号。本文采取半均匀采样技巧，突破了这一限制。对满足ｆ_ｓ≥ｆ_ｅ／３的宽带带通信号，建立了精确的恢复公式，采样率为４ｆｅ／３，低于Ｎｙｑｕｉｓｔ率；如果ｆ_ｓ＜ｆ_ｅ／３，用ｔｉｌｉｎｇ分析技术可以证明无论是均匀还是半均匀采样，最低采样率必然是２ｆ_ｅ。这表明本文所给出的宽带条件是最优的。

The traditional sampling theorem for band-pass signals holds only for narrow band case f>f/2 provided the cut-off frequencies are fand fe, otherwise one can only sample with at ho Nyquist rate. We im prove this' theory by introducing a semi-uniform Samping scheme for wide band-pass signals under the assumption that fs fe/3, in which the the reduced sampling rate is 4fe/3, which is las than Nyquist Nyquist 2fe. If this condition breads down, a tiling analysis assocthe with spectrum theory asserts that we must return back to Shannon's theo- ry. Thus our result is optimal, and the conditionf_e;>f_e/3 can not be tmproved.